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Unitarity and Holography in Gravitational Physics

Donald Marolf

TL;DR

The work addresses whether information is lost in black hole evaporation by exploiting the boundary-term nature of gravity's Hamiltonian, suggesting that asymptotic fields store full information in a holographic fashion. It develops perturbative holography in both asymptotically flat and AdS spacetimes, showing that boundary algebras near infinity are complete at perturbative order, and argues that unitarity can extend non-perturbatively if the same completeness holds. In AdS, the analysis yields a stronger notion of boundary unitarity when the boundary Hamiltonian is self-adjoint, linking to AdS/CFT intuition. Collectively, these results frame information storage and transfer in quantum gravity as governed by boundary data and energy conservation, offering a coherent path toward reconciling locality, holography, and unitarity in gravitational theories.

Abstract

Because the gravitational Hamiltonian is a pure boundary term on-shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and non-perturbative quantum gravity. In perturbation theory about an asymptotically flat collapsing black hole, the algebra generated by asymptotic fields on future null infinity within any neighborhood of spacelike infinity contains a complete set of observables. Assuming that the same algebra remains complete at the non-perturbative quantum level, we argue that either 1) the S-matrix is unitary or 2) the dynamics in the region near timelike, null, and spacelike infinity is not described by perturbative quantum gravity about flat space. We also consider perturbation theory about a collapsing asymptotically anti-de Sitter (AdS) black hole, where we show that the algebra of boundary observables within any neighborhood of any boundary Cauchy surface is similarly complete. Whether or not this algebra continues to be complete non-perturbatively, the assumption that the Hamiltonian remains a boundary term implies that information available at the AdS boundary at any one time t_1 remains present at this boundary at any other time t_2.

Unitarity and Holography in Gravitational Physics

TL;DR

The work addresses whether information is lost in black hole evaporation by exploiting the boundary-term nature of gravity's Hamiltonian, suggesting that asymptotic fields store full information in a holographic fashion. It develops perturbative holography in both asymptotically flat and AdS spacetimes, showing that boundary algebras near infinity are complete at perturbative order, and argues that unitarity can extend non-perturbatively if the same completeness holds. In AdS, the analysis yields a stronger notion of boundary unitarity when the boundary Hamiltonian is self-adjoint, linking to AdS/CFT intuition. Collectively, these results frame information storage and transfer in quantum gravity as governed by boundary data and energy conservation, offering a coherent path toward reconciling locality, holography, and unitarity in gravitational theories.

Abstract

Because the gravitational Hamiltonian is a pure boundary term on-shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and non-perturbative quantum gravity. In perturbation theory about an asymptotically flat collapsing black hole, the algebra generated by asymptotic fields on future null infinity within any neighborhood of spacelike infinity contains a complete set of observables. Assuming that the same algebra remains complete at the non-perturbative quantum level, we argue that either 1) the S-matrix is unitary or 2) the dynamics in the region near timelike, null, and spacelike infinity is not described by perturbative quantum gravity about flat space. We also consider perturbation theory about a collapsing asymptotically anti-de Sitter (AdS) black hole, where we show that the algebra of boundary observables within any neighborhood of any boundary Cauchy surface is similarly complete. Whether or not this algebra continues to be complete non-perturbatively, the assumption that the Hamiltonian remains a boundary term implies that information available at the AdS boundary at any one time t_1 remains present at this boundary at any other time t_2.

Paper Structure

This paper contains 7 sections, 17 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quantum Gravity in Asymptotically Flat Space
  3. The Holographic nature of perturbative gravity
  4. Non-perturbative gravity and Unitarity of the S-matrix
  5. Asymptotically AdS Quantum Gravity
  6. Discussion
  7. Tail Corrections in the Perturbative Holography Argument for Asymptotically Flat Spacetimes

Figures (2)

  • Figure 1: The spacetime is flat before advanced time $v_0$, but the formation of a black hole prohibits a regular $i^+$.
  • Figure 2: As $\tau \rightarrow +\infty$, operators at $v-\tau$ on $I^-$ can be written in terms of operators on $I^+$ before retarded time $u_1$.